Any way to customize the color of the text input cursor?
I do not think that is possible. I checked the general 'User Interface' theme section, the 'Text Editor' cursor colour and I even went so far as to check any items which are blue in the other theme settings just in case they might affect it. Unfortunately none of them did. I also checked other areas of the user preferences as there are a few theme-like settings in other sections but to no avail. While the majority of Blender's interface is customisable, there are a few things which aren't and I think this is one of them.